Internal problem ID [6838]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 106.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.179 (sec). Leaf size: 42
dsolve(2*x^2*(2+x^2)*diff(y(x),x$2)-x*(12-7*x^2)*diff(y(x),x)+(7+3*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{\frac {7}{2}}}{\left (x^{2}+2\right )^{2} \left (2 x^{2}+4\right )^{\frac {1}{4}}}+c_{2} \sqrt {x}\, \hypergeom \left (\left [\frac {3}{4}, 1\right ], \left [-\frac {1}{2}\right ], -\frac {x^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 10.04 (sec). Leaf size: 57
DSolve[2*x^2*(2+x^2)*y''[x]-x*(12-7*x^2)*y'[x]+(7+3*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {x} \left (3 c_1 x^3-2 \sqrt [4]{2} c_2 \, _2F_1\left (-\frac {3}{2},-\frac {5}{4};-\frac {1}{2};-\frac {x^2}{2}\right )\right )}{3 \left (x^2+2\right )^{9/4}} \\ \end{align*}